**3.2 Flow and viscosity behaviour characteristics**

The flow curves for reactor fluids A-E (Figures 2−3) indicated different flow behaviour according to the definitions by Schramm (2000). A Newtonian behaviour of reactors A and D, fed with slaughter house waste and wheat stillage, respectively, was illustrated where the exerted shear stress was almost proportional to the induced shear rate. However, a small yield stress of 0.2 Pa and 0.3 Pa were detected, indicating a pseudo-Newtonian behaviour.

Fluids from reactor B, receiving biosludge from paper mill industry 1 as substrate, indicated an unusual performance at the beginning of the rheogram with decreasing shear stress, thereafter a linear increase in shear stress. A yield stress of 14 Pa was detected. A space

0 100 200 300 400 500 600 700 **1/s** 800

**.**

Fig. 3. Rheogram - flow and viscosity curves for reactors D (▲; ●) and E (▲; ●) with a threestep protocol. Flow curves illustrating shear stress (; Pa) vs shear rate (; s-1) and viscosity

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 **1/s** 800

Fig. 4. Rheogram - flow and viscosity curves for reactors A (▲;●), B (▲;●) and C (▲;●) with a three-step protocol. Flow curves illustrating shear stress (; Pa) vs shear rate (; s-1) and

**Shear Rate .**

viscosity curves illustrating dynamic viscosity (; Pa\*s) vs shear stress (; s-1).

**Shear Rate** 

curves illustrating dynamic viscosity (; Pa\*s) vs shear stress (; s-1).

10-3

0,001

0,01

0,1

1

10

100

1 000

10 000

100 000

1 000 000 **Pa·s**

10-2

10-1

100

101

102

103

104

105 **Pa·s**

30 **Pa**

30 **Pa**

between the curves was noticeable when the shear rate increased and afterwards decreased for reactor B (Fig. 2). This area describes the degree of thixotropy of this fluid, which means that the increase of this area is related to the amount of energy required to breaking down the thixotropic structure. Thus, the flow curves obtained with the three-step protocol indicated a thixotropic behaviour of reactor fluid B.

Fig. 2. Rheogram - flow curves illustrating shear stress (; Pa) vs shear rate (; s-1) for fluids from reactor A (▲), B (▲) and C (▲) with a three-step protocol.

Reactors C and E revealed viscoplastic behaviours, i.e. a pseudoplastic behaviour with yield stress. Reactor C, fed with biosludge from paper mill industry 2, showed a yield stress of 4 Pa (Fig. 2), and reactor E, receiving cereal residues, a yield point of 4.5 Pa (Fig. 3). The yield stress is defined as the force that a fluid must overcome in order to start flowing (Spinosa & Lotito, 2003). Also for reactor E, a small space between the curves was noticeable when the shear rate increased and afterwards decreased (Fig. 3). This area difference might indicate some degree of thixotropy.


Table 2. The flow and viscosity curves for reactor fluids A-E indicated different fluid behaviour according to Schramm (2000).

between the curves was noticeable when the shear rate increased and afterwards decreased for reactor B (Fig. 2). This area describes the degree of thixotropy of this fluid, which means that the increase of this area is related to the amount of energy required to breaking down the thixotropic structure. Thus, the flow curves obtained with the three-step protocol

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 **1/s** 800

**.**

**Shear Rate** 

Reactor Flow curve behaviour Viscosity curve behaviour

B Thixotropic Thixotropic C Viscoplastic Viscoplastic

E Viscoplastic Viscoplastic

A Newtonian; pseudo-Newtonian Viscoplastic (pseudo-Newtonian)

D Newtonian; pseudo-Newtonian Pseudoplastic or viscoplastic

Table 2. The flow and viscosity curves for reactor fluids A-E indicated different fluid

from reactor A (▲), B (▲) and C (▲) with a three-step protocol.

Fig. 2. Rheogram - flow curves illustrating shear stress (; Pa) vs shear rate (; s-1) for fluids

Reactors C and E revealed viscoplastic behaviours, i.e. a pseudoplastic behaviour with yield stress. Reactor C, fed with biosludge from paper mill industry 2, showed a yield stress of 4 Pa (Fig. 2), and reactor E, receiving cereal residues, a yield point of 4.5 Pa (Fig. 3). The yield stress is defined as the force that a fluid must overcome in order to start flowing (Spinosa & Lotito, 2003). Also for reactor E, a small space between the curves was noticeable when the shear rate increased and afterwards decreased (Fig. 3). This area difference might indicate

indicated a thixotropic behaviour of reactor fluid B.

some degree of thixotropy.

behaviour according to Schramm (2000).

30 **Pa**

Fig. 3. Rheogram - flow and viscosity curves for reactors D (▲; ●) and E (▲; ●) with a threestep protocol. Flow curves illustrating shear stress (; Pa) vs shear rate (; s-1) and viscosity curves illustrating dynamic viscosity (; Pa\*s) vs shear stress (; s-1).

Fig. 4. Rheogram - flow and viscosity curves for reactors A (▲;●), B (▲;●) and C (▲;●) with a three-step protocol. Flow curves illustrating shear stress (; Pa) vs shear rate (; s-1) and viscosity curves illustrating dynamic viscosity (; Pa\*s) vs shear stress (; s-1).

Fig. 5. Rheogram – shear stress (; Pa) vs shear rate (; s-1) of reactor B. Four measurements of the same sample were made after different sample resting times (1st▲; 2nd▲; 3rd▲;

Also, the Herchel-Bulkley model indicated that reactor fluid A performed as a pseudo-Newtonian fluid called Bingham plastic, since the yield stress-value was > 0 (0.24 Pa) and a flow behaviour index of 1.06 (Table 4). Results obtained by the Ostwald and Bingham models confirmed a Bingham plastic behaviour of reactor A. However, since the 0-value was almost 0 and the n-value 1 it was also closely performing as a Newtonian fluid which is consistent with the flow curve appearance (Fig. 2). However, when studying the viscosity curve (Fig. 4) the results showed an initial viscosity decrease and then a constant viscosity

The Herschel-Bulkley and Ostwald models both indicated a pseudoplastic behaviour of reactor D, since the 0-value was 0 and n < 1 (Table 4). The Bingham model gave a yield stress of 0.33 Pa which did not indicate Newtonian or Bingham plastic behaviour. Thus, the

Reactor B was hard to define also when modelling the rheogram data values of figure 4. The regression values were low for all three mathematical models (Table 4). However, the Herschel-Bulkely model had a flow behaviour index n>1 indicating that the fluid acted as a shear thickening (dilatant) fluid, but the Ostwald and Bingham models indicated pseudoplastic and Bingham plastic behaviours, respectively. When the static yield stress appeared in the reactor B rheogram (Figures 2 and 4), the flow behaviour index showed shear thickening fluid behaviour (n=3.4) and a limit viscosity of 8 mPa\*s. This also

common results for reactor D strongest indicate a pseudoplastic fluid behaviour.

4th ▲).

**3.3 Mathematical modeling** 

indicating a pseudo-Newtonian fluid behaviour.

The viscosity curves (Figures 3−4) did almost correspond to the flow curve behaviour for the investigated biogas reactor fluids (Table 2). Using the scheme by Schramm (2000) the viscosity curves for reactor A indicated a viscoplastic liquid and for reactor D a viscoplastic or pseudoplastic liquid. The viscosity initially dropped very quickly for reactor A, specifically indicating Bingham viscoplastic fluids with pseudo-Newtonian behaviour. Generally for reactors A−E, the viscosity decreased with increasing shear rate, until it reached its limit viscosities (Table 3).


Table 3. The initial dynamic viscosity and the limit viscosity obtained during interval 1 in the 3-step protocol analysis for each reactor fluid.

The limit viscosities ranged 6−36 mPa\*s with the highest value for reactor E (Table 3). However, the limit viscosity was similar for reactor C and E despite a difference in TS (%). The dynamic viscosity ranged 18−443 mPa\*s for the reactor fluids (Table 3). The reactors A and D showed lower dynamic viscosity values compared to reactor B, C and E, possibly due to their pseudo-Newtonian behaviour. Also, there was a difference in dynamic viscosity between reactor fluids B and C both receiving biosludge with similar TS (%) but coming from two different paper mill industries in Sweden. Thus, the results demonstrated that similar TS values do not necessarily correspond to similar dynamic or limit viscosity values. This contradicts the results presented by Tixier and Guibad (2003), who reported that an increase in TS for activated sludge corresponded to a higher limit viscosity and higher yield stress. Nor, did biosludge from two different Swedish pulp- and paper mill industries with similar TS give similar viscosity values.

Samples from reactor B showed different rheological behaviour depending on when they were measured. The yield stress and viscosity increased when the reactor fluids had been stored and resting compared to when analyzed immediately after sampling, indicating thixotropic behaviour. Figure 5 illustrates how the B reactor fluid after been resting for 48 hours showed a resistance to flow, known as static yield stress. This value (24 Pa) decreased until it reached the dynamic yield stress (7 Pa), which was the value needed in order to become liquid and start flowing. When the analysis was done right after the first measurement (Second measurement), the fluid had already been stirred, so the two different structures that form the resistance to flow were now mixed and no static yield stress was detected. The static yield stress might be initiated by several factors, e.g. weakness of the fluid structure, low mixed liquid solid suspension (MLSS) concentration, small size of particles and poor dewater ability (Pevere *et al.* 2006).

The viscosity curves (Figures 3−4) did almost correspond to the flow curve behaviour for the investigated biogas reactor fluids (Table 2). Using the scheme by Schramm (2000) the viscosity curves for reactor A indicated a viscoplastic liquid and for reactor D a viscoplastic or pseudoplastic liquid. The viscosity initially dropped very quickly for reactor A, specifically indicating Bingham viscoplastic fluids with pseudo-Newtonian behaviour. Generally for reactors A−E, the viscosity decreased with increasing shear rate, until it

(%)

A Slaughter house waste 3.9 18 6 B Biosludge paper mill industry 1 3.8 436 8 C Biosludge paper mill industry 2 3.7 267 29 D Wheat stillage 3.0 33 6 E Cereal residues 7.7 443 36 Table 3. The initial dynamic viscosity and the limit viscosity obtained during interval 1 in

The limit viscosities ranged 6−36 mPa\*s with the highest value for reactor E (Table 3). However, the limit viscosity was similar for reactor C and E despite a difference in TS (%). The dynamic viscosity ranged 18−443 mPa\*s for the reactor fluids (Table 3). The reactors A and D showed lower dynamic viscosity values compared to reactor B, C and E, possibly due to their pseudo-Newtonian behaviour. Also, there was a difference in dynamic viscosity between reactor fluids B and C both receiving biosludge with similar TS (%) but coming from two different paper mill industries in Sweden. Thus, the results demonstrated that similar TS values do not necessarily correspond to similar dynamic or limit viscosity values. This contradicts the results presented by Tixier and Guibad (2003), who reported that an increase in TS for activated sludge corresponded to a higher limit viscosity and higher yield stress. Nor, did biosludge from two different Swedish pulp- and paper mill industries with

Samples from reactor B showed different rheological behaviour depending on when they were measured. The yield stress and viscosity increased when the reactor fluids had been stored and resting compared to when analyzed immediately after sampling, indicating thixotropic behaviour. Figure 5 illustrates how the B reactor fluid after been resting for 48 hours showed a resistance to flow, known as static yield stress. This value (24 Pa) decreased until it reached the dynamic yield stress (7 Pa), which was the value needed in order to become liquid and start flowing. When the analysis was done right after the first measurement (Second measurement), the fluid had already been stirred, so the two different structures that form the resistance to flow were now mixed and no static yield stress was detected. The static yield stress might be initiated by several factors, e.g. weakness of the fluid structure, low mixed liquid solid suspension (MLSS) concentration, small size of

Dynamic viscosity (mPa\*s)

Limit viscosity (mPa\*s)

reached its limit viscosities (Table 3).

Reactor Treated substrate TS

the 3-step protocol analysis for each reactor fluid.

similar TS give similar viscosity values.

particles and poor dewater ability (Pevere *et al.* 2006).

Fig. 5. Rheogram – shear stress (; Pa) vs shear rate (; s-1) of reactor B. Four measurements of the same sample were made after different sample resting times (1st▲; 2nd▲; 3rd▲; 4th ▲).
